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Polytope of Type {60,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,4}*1920d
if this polytope has a name.
Group : SmallGroup(1920,239398)
Rank : 3
Schlafli Type : {60,4}
Number of vertices, edges, etc : 240, 480, 16
Order of s0s1s2 : 60
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {60,4}*960b, {30,4}*960b, {60,4}*960c
   4-fold quotients : {60,4}*480a, {60,4}*480b, {60,4}*480c, {30,4}*480
   5-fold quotients : {12,4}*384d
   8-fold quotients : {60,2}*240, {30,4}*240a, {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {12,4}*192b, {6,4}*192b, {12,4}*192c
   12-fold quotients : {20,4}*160
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {12,4}*96a, {12,4}*96b, {12,4}*96c, {6,4}*96
   24-fold quotients : {20,2}*80, {10,4}*80
   32-fold quotients : {15,2}*60
   40-fold quotients : {12,2}*48, {6,4}*48a, {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   60-fold quotients : {4,4}*32
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   120-fold quotients : {2,4}*16, {4,2}*16
   160-fold quotients : {3,2}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)
( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)
( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)
( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)
( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)
( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)(129,133)
(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)(145,177)
(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)(153,169)
(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)(183,184)
(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)(192,195)
(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)(208,239)
(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)(216,231)
(217,225)(218,226)(219,228)(220,227)(241,301)(242,302)(243,304)(244,303)
(245,317)(246,318)(247,320)(248,319)(249,313)(250,314)(251,316)(252,315)
(253,309)(254,310)(255,312)(256,311)(257,305)(258,306)(259,308)(260,307)
(261,341)(262,342)(263,344)(264,343)(265,357)(266,358)(267,360)(268,359)
(269,353)(270,354)(271,356)(272,355)(273,349)(274,350)(275,352)(276,351)
(277,345)(278,346)(279,348)(280,347)(281,321)(282,322)(283,324)(284,323)
(285,337)(286,338)(287,340)(288,339)(289,333)(290,334)(291,336)(292,335)
(293,329)(294,330)(295,332)(296,331)(297,325)(298,326)(299,328)(300,327)
(361,421)(362,422)(363,424)(364,423)(365,437)(366,438)(367,440)(368,439)
(369,433)(370,434)(371,436)(372,435)(373,429)(374,430)(375,432)(376,431)
(377,425)(378,426)(379,428)(380,427)(381,461)(382,462)(383,464)(384,463)
(385,477)(386,478)(387,480)(388,479)(389,473)(390,474)(391,476)(392,475)
(393,469)(394,470)(395,472)(396,471)(397,465)(398,466)(399,468)(400,467)
(401,441)(402,442)(403,444)(404,443)(405,457)(406,458)(407,460)(408,459)
(409,453)(410,454)(411,456)(412,455)(413,449)(414,450)(415,452)(416,451)
(417,445)(418,446)(419,448)(420,447);;
s1 := (  1,265)(  2,268)(  3,267)(  4,266)(  5,261)(  6,264)(  7,263)(  8,262)
(  9,277)( 10,280)( 11,279)( 12,278)( 13,273)( 14,276)( 15,275)( 16,274)
( 17,269)( 18,272)( 19,271)( 20,270)( 21,245)( 22,248)( 23,247)( 24,246)
( 25,241)( 26,244)( 27,243)( 28,242)( 29,257)( 30,260)( 31,259)( 32,258)
( 33,253)( 34,256)( 35,255)( 36,254)( 37,249)( 38,252)( 39,251)( 40,250)
( 41,285)( 42,288)( 43,287)( 44,286)( 45,281)( 46,284)( 47,283)( 48,282)
( 49,297)( 50,300)( 51,299)( 52,298)( 53,293)( 54,296)( 55,295)( 56,294)
( 57,289)( 58,292)( 59,291)( 60,290)( 61,325)( 62,328)( 63,327)( 64,326)
( 65,321)( 66,324)( 67,323)( 68,322)( 69,337)( 70,340)( 71,339)( 72,338)
( 73,333)( 74,336)( 75,335)( 76,334)( 77,329)( 78,332)( 79,331)( 80,330)
( 81,305)( 82,308)( 83,307)( 84,306)( 85,301)( 86,304)( 87,303)( 88,302)
( 89,317)( 90,320)( 91,319)( 92,318)( 93,313)( 94,316)( 95,315)( 96,314)
( 97,309)( 98,312)( 99,311)(100,310)(101,345)(102,348)(103,347)(104,346)
(105,341)(106,344)(107,343)(108,342)(109,357)(110,360)(111,359)(112,358)
(113,353)(114,356)(115,355)(116,354)(117,349)(118,352)(119,351)(120,350)
(121,385)(122,388)(123,387)(124,386)(125,381)(126,384)(127,383)(128,382)
(129,397)(130,400)(131,399)(132,398)(133,393)(134,396)(135,395)(136,394)
(137,389)(138,392)(139,391)(140,390)(141,365)(142,368)(143,367)(144,366)
(145,361)(146,364)(147,363)(148,362)(149,377)(150,380)(151,379)(152,378)
(153,373)(154,376)(155,375)(156,374)(157,369)(158,372)(159,371)(160,370)
(161,405)(162,408)(163,407)(164,406)(165,401)(166,404)(167,403)(168,402)
(169,417)(170,420)(171,419)(172,418)(173,413)(174,416)(175,415)(176,414)
(177,409)(178,412)(179,411)(180,410)(181,445)(182,448)(183,447)(184,446)
(185,441)(186,444)(187,443)(188,442)(189,457)(190,460)(191,459)(192,458)
(193,453)(194,456)(195,455)(196,454)(197,449)(198,452)(199,451)(200,450)
(201,425)(202,428)(203,427)(204,426)(205,421)(206,424)(207,423)(208,422)
(209,437)(210,440)(211,439)(212,438)(213,433)(214,436)(215,435)(216,434)
(217,429)(218,432)(219,431)(220,430)(221,465)(222,468)(223,467)(224,466)
(225,461)(226,464)(227,463)(228,462)(229,477)(230,480)(231,479)(232,478)
(233,473)(234,476)(235,475)(236,474)(237,469)(238,472)(239,471)(240,470);;
s2 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)
( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)
( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)
( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)
( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)
(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)
(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)
(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)
(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)
(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)
(241,362)(242,361)(243,364)(244,363)(245,366)(246,365)(247,368)(248,367)
(249,370)(250,369)(251,372)(252,371)(253,374)(254,373)(255,376)(256,375)
(257,378)(258,377)(259,380)(260,379)(261,382)(262,381)(263,384)(264,383)
(265,386)(266,385)(267,388)(268,387)(269,390)(270,389)(271,392)(272,391)
(273,394)(274,393)(275,396)(276,395)(277,398)(278,397)(279,400)(280,399)
(281,402)(282,401)(283,404)(284,403)(285,406)(286,405)(287,408)(288,407)
(289,410)(290,409)(291,412)(292,411)(293,414)(294,413)(295,416)(296,415)
(297,418)(298,417)(299,420)(300,419)(301,422)(302,421)(303,424)(304,423)
(305,426)(306,425)(307,428)(308,427)(309,430)(310,429)(311,432)(312,431)
(313,434)(314,433)(315,436)(316,435)(317,438)(318,437)(319,440)(320,439)
(321,442)(322,441)(323,444)(324,443)(325,446)(326,445)(327,448)(328,447)
(329,450)(330,449)(331,452)(332,451)(333,454)(334,453)(335,456)(336,455)
(337,458)(338,457)(339,460)(340,459)(341,462)(342,461)(343,464)(344,463)
(345,466)(346,465)(347,468)(348,467)(349,470)(350,469)(351,472)(352,471)
(353,474)(354,473)(355,476)(356,475)(357,478)(358,477)(359,480)(360,479);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(480)!(  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)
( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)
( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)
( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)
( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)
( 98,106)( 99,108)(100,107)(123,124)(125,137)(126,138)(127,140)(128,139)
(129,133)(130,134)(131,136)(132,135)(141,161)(142,162)(143,164)(144,163)
(145,177)(146,178)(147,180)(148,179)(149,173)(150,174)(151,176)(152,175)
(153,169)(154,170)(155,172)(156,171)(157,165)(158,166)(159,168)(160,167)
(183,184)(185,197)(186,198)(187,200)(188,199)(189,193)(190,194)(191,196)
(192,195)(201,221)(202,222)(203,224)(204,223)(205,237)(206,238)(207,240)
(208,239)(209,233)(210,234)(211,236)(212,235)(213,229)(214,230)(215,232)
(216,231)(217,225)(218,226)(219,228)(220,227)(241,301)(242,302)(243,304)
(244,303)(245,317)(246,318)(247,320)(248,319)(249,313)(250,314)(251,316)
(252,315)(253,309)(254,310)(255,312)(256,311)(257,305)(258,306)(259,308)
(260,307)(261,341)(262,342)(263,344)(264,343)(265,357)(266,358)(267,360)
(268,359)(269,353)(270,354)(271,356)(272,355)(273,349)(274,350)(275,352)
(276,351)(277,345)(278,346)(279,348)(280,347)(281,321)(282,322)(283,324)
(284,323)(285,337)(286,338)(287,340)(288,339)(289,333)(290,334)(291,336)
(292,335)(293,329)(294,330)(295,332)(296,331)(297,325)(298,326)(299,328)
(300,327)(361,421)(362,422)(363,424)(364,423)(365,437)(366,438)(367,440)
(368,439)(369,433)(370,434)(371,436)(372,435)(373,429)(374,430)(375,432)
(376,431)(377,425)(378,426)(379,428)(380,427)(381,461)(382,462)(383,464)
(384,463)(385,477)(386,478)(387,480)(388,479)(389,473)(390,474)(391,476)
(392,475)(393,469)(394,470)(395,472)(396,471)(397,465)(398,466)(399,468)
(400,467)(401,441)(402,442)(403,444)(404,443)(405,457)(406,458)(407,460)
(408,459)(409,453)(410,454)(411,456)(412,455)(413,449)(414,450)(415,452)
(416,451)(417,445)(418,446)(419,448)(420,447);
s1 := Sym(480)!(  1,265)(  2,268)(  3,267)(  4,266)(  5,261)(  6,264)(  7,263)
(  8,262)(  9,277)( 10,280)( 11,279)( 12,278)( 13,273)( 14,276)( 15,275)
( 16,274)( 17,269)( 18,272)( 19,271)( 20,270)( 21,245)( 22,248)( 23,247)
( 24,246)( 25,241)( 26,244)( 27,243)( 28,242)( 29,257)( 30,260)( 31,259)
( 32,258)( 33,253)( 34,256)( 35,255)( 36,254)( 37,249)( 38,252)( 39,251)
( 40,250)( 41,285)( 42,288)( 43,287)( 44,286)( 45,281)( 46,284)( 47,283)
( 48,282)( 49,297)( 50,300)( 51,299)( 52,298)( 53,293)( 54,296)( 55,295)
( 56,294)( 57,289)( 58,292)( 59,291)( 60,290)( 61,325)( 62,328)( 63,327)
( 64,326)( 65,321)( 66,324)( 67,323)( 68,322)( 69,337)( 70,340)( 71,339)
( 72,338)( 73,333)( 74,336)( 75,335)( 76,334)( 77,329)( 78,332)( 79,331)
( 80,330)( 81,305)( 82,308)( 83,307)( 84,306)( 85,301)( 86,304)( 87,303)
( 88,302)( 89,317)( 90,320)( 91,319)( 92,318)( 93,313)( 94,316)( 95,315)
( 96,314)( 97,309)( 98,312)( 99,311)(100,310)(101,345)(102,348)(103,347)
(104,346)(105,341)(106,344)(107,343)(108,342)(109,357)(110,360)(111,359)
(112,358)(113,353)(114,356)(115,355)(116,354)(117,349)(118,352)(119,351)
(120,350)(121,385)(122,388)(123,387)(124,386)(125,381)(126,384)(127,383)
(128,382)(129,397)(130,400)(131,399)(132,398)(133,393)(134,396)(135,395)
(136,394)(137,389)(138,392)(139,391)(140,390)(141,365)(142,368)(143,367)
(144,366)(145,361)(146,364)(147,363)(148,362)(149,377)(150,380)(151,379)
(152,378)(153,373)(154,376)(155,375)(156,374)(157,369)(158,372)(159,371)
(160,370)(161,405)(162,408)(163,407)(164,406)(165,401)(166,404)(167,403)
(168,402)(169,417)(170,420)(171,419)(172,418)(173,413)(174,416)(175,415)
(176,414)(177,409)(178,412)(179,411)(180,410)(181,445)(182,448)(183,447)
(184,446)(185,441)(186,444)(187,443)(188,442)(189,457)(190,460)(191,459)
(192,458)(193,453)(194,456)(195,455)(196,454)(197,449)(198,452)(199,451)
(200,450)(201,425)(202,428)(203,427)(204,426)(205,421)(206,424)(207,423)
(208,422)(209,437)(210,440)(211,439)(212,438)(213,433)(214,436)(215,435)
(216,434)(217,429)(218,432)(219,431)(220,430)(221,465)(222,468)(223,467)
(224,466)(225,461)(226,464)(227,463)(228,462)(229,477)(230,480)(231,479)
(232,478)(233,473)(234,476)(235,475)(236,474)(237,469)(238,472)(239,471)
(240,470);
s2 := Sym(480)!(  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)
( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)
( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)
( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)
( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)
(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)
(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)
(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)
(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)
(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)
(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)
(239,240)(241,362)(242,361)(243,364)(244,363)(245,366)(246,365)(247,368)
(248,367)(249,370)(250,369)(251,372)(252,371)(253,374)(254,373)(255,376)
(256,375)(257,378)(258,377)(259,380)(260,379)(261,382)(262,381)(263,384)
(264,383)(265,386)(266,385)(267,388)(268,387)(269,390)(270,389)(271,392)
(272,391)(273,394)(274,393)(275,396)(276,395)(277,398)(278,397)(279,400)
(280,399)(281,402)(282,401)(283,404)(284,403)(285,406)(286,405)(287,408)
(288,407)(289,410)(290,409)(291,412)(292,411)(293,414)(294,413)(295,416)
(296,415)(297,418)(298,417)(299,420)(300,419)(301,422)(302,421)(303,424)
(304,423)(305,426)(306,425)(307,428)(308,427)(309,430)(310,429)(311,432)
(312,431)(313,434)(314,433)(315,436)(316,435)(317,438)(318,437)(319,440)
(320,439)(321,442)(322,441)(323,444)(324,443)(325,446)(326,445)(327,448)
(328,447)(329,450)(330,449)(331,452)(332,451)(333,454)(334,453)(335,456)
(336,455)(337,458)(338,457)(339,460)(340,459)(341,462)(342,461)(343,464)
(344,463)(345,466)(346,465)(347,468)(348,467)(349,470)(350,469)(351,472)
(352,471)(353,474)(354,473)(355,476)(356,475)(357,478)(358,477)(359,480)
(360,479);
poly := sub<Sym(480)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope